Problem: $A$ $B$ $C$ If: $ AC = 53$, $ AB = 3x + 4$, and $ BC = 6x + 4$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {3x + 4} + {6x + 4} = {53}$ Combine like terms: $ 9x + 8 = {53}$ Subtract $8$ from both sides: $ 9x = 45$ Divide both sides by $9$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $BC$ $ BC = 6({5}) + 4$ Simplify: $ {BC = 30 + 4}$ Simplify to find ${BC}$ : $ {BC = 34}$